1. Field of the Invention
This invention relates to seismic data processing and particularly to an improved method for migrating seismic data.
2. Discussion of the Prior Art
Seismic surveys are conducted in a variety of environments and over a variety of terrains. The surveys are often conducted in regions having topographic relief on the orders of tens or hundreds of meters. Valleys, canyons, hills, and irregular water bottoms may cause distortion in the data. When the data are processed and displayed, the data have been time-adjusted as if the recording surface was horizontal. That is to say that surface irregularities associated with the topographic relief often are not handled properly in processing the data.
In regions of slight topographic relief, minor changes in elevation do not present much of a problem and, for all practical purposes, processes such as migration may be performed without any adverse effects. However, when the data have been collected along a survey line having substantial topographic relief, migration may not be optimum until the data have been shifted relative to some fixed or variable datum. The reason for shifting to a datum before migration is apparent to one skilled in the art and will not be discussed herein in great detail, but in general, migration algorithms assume that a sloping surface is a flat surface and will migrate the data at some angle to the gravitational vertical, producing an incorrect image of the subsurface. In addition to the problem of surface irregularities the problem of processing the data from some datum different from the recording surface arises. Clients may desire that the data be displayed from some elevation other than the surface elevation. Conventionally shifting the data to the desired datum and performing a migration results in under- or over-migrated seismic data.
It is common practice in seismic data processing to deal with elevation changes along a seismic line by shifting the data in time so that the zero time is identified with a flat datum--a precess known as elevation-static corrections. The required time shift is calculated as the vertical two-way travel time through the layer between the datum and the actual recording surface. A difficulty with this technique is the choice of the datum elevation. When the datum lies above the surface, a fictitious earth layer must be inserted between the surface and the datum. When the datum lies below the surface, near-surface layers may be lost in applying the elevation-static corrections.
Another difficulty lies in the choice of a migration-velocity field. Velocities used for migration should be governed by interval velocity in the subsurface. Because simple time-shifting does not properly adjust event move-out, migration with the true earth velocity can lead to errors in migration results. Consequently, the migration-velocity field may require artificial adjustments to compensate for the artifacts--a compromise solution that attempts to offset one error by another.
Despite these difficulties with elevation-static corrections, strong motivations exist for placing data on a horizontal surface. Most migration algorithms, for example, require input from a flat surface for efficient performance. An accurate solution to the problem of varying elevation is to propagate the wave field from the recording surface to a specified flat datum using wave-equation datuming. The accurate but computationally intensive method was first proposed by R. T. Berryhill in a paper titled, "Wave-equation datuming" appearing in Geophysics, Volume 44, pages 1329-1344.
Another problem is encountered in marine seismic exploration where the ocean bottom is irregular. This does not pose the exact problem as recording along an irregular surface since the streamer cable is substantially horizontal. However, the irregular water bottom situation produces a complex image even when the subsurface structure is rather uncomplicated. This is because Snell's Law governs the ray paths of the signals as the pass from the higher velocity sediments into the lower velocity water body.
Techniques have been proposed to solve these problems. Wave-equation datuming, used in a manner known as "layer replacement", may be used to image the irregular water bottom to a horizontal surface as proposed by Berryhill, but as mentioned earlier, this is an expensive procedure because of the computational time necessary to perform the calculations. Another technique which may be used is called "wave theoretical depth migration." This technique has the disadvantages of being an expensive computation as well as being extremely sensitive to minor changes in migration velocity.
Each of the above techniques previously and presently used to migrate seismic data will be discussed in greater detail below. This discussion is provided only for the purpose of illustrating to the reader that there has been a long felt yet unsolved need for a relatively inexpensive method of migrating seismic data having been elevation-static corrected, and yet remaining within the realm of conventional data processing.